Evolution of cardiac calcium waves from stochastic calcium sparks

We present a model that provides a unified framework for studying Ca²⁺ sparks and Ca²⁺ waves in cardiac cells. The model is novel in combining 1) use of large currents (∼20 pA) through the Ca²⁺ release units (CRUs) of the sarcoplasmic reticulum (SR); 2) stochastic Ca²⁺ release (or firing) of CRUs; 3) discrete, asymmetric distribution of CRUs along the longitudinal (separation distance of 2 μm) and transverse (separated by 0.4-0.8 μm) directions of the cell; and 4) anisotropic diffusion of Ca²⁺ and fluorescent indicator to study the evolution of Ca²⁺ waves from Ca²⁺ sparks. The model mimics the important features of Ca²⁺ sparks and Ca²⁺ waves in terms of the spontaneous spark rate, the Ca²⁺ wave velocity, and the pattern of wave propagation. Importantly, these features are reproduced when using experimentally measured values for the CRU Ca²⁺ sensitivity (∼15 μM). Stochastic control of CRU firing is important because it imposes constraints on the Ca²⁺ sensitivity of the CRU. Even with moderate (∼5 μM) Ca²⁺ sensitivity the very high spontaneous spark rate triggers numerous Ca²⁺ waves. In contrast, a single Ca²⁺ wave with arbitrarily large velocity can exist in a deterministic model when the CRU Ca²⁺ sensitivity is sufficiently high. The combination of low CRU Ca²⁺ sensitivity (∼15 μM), high cytosolic Ca²⁺ buffering capacity, and the spatial separation of CRUs help control the inherent instability of SR Ca²⁺ release. This allows Ca²⁺ waves to form and propagate given a sufficiently large initiation region, but prevents a single spark or a small group of sparks from triggering a wave.